There are several ways to do this and so it becomes a matter of personal preference. The Russian join works well with cotton yarn and it's shown under Tips on the Free Videos tab at the top of the page.
If you're using two strands held together for the blanket, you need not join both new strands at the same time. You can overlap one old strand and one new strand for a stitch or two and then weave in the ends. Both techniques give a double thickness of yarn for a few sts but it's unnoticeable.
Lovely blanket!http://www.ravelry.com/patterns/libr...y-baby-blanket

but I unravel the old end a few inches, and the new end a few inches and then braid them tightly together then trim the ends so it looks like one continuous piece of yarn - the braided section is usually only and inch/2 inches (depending on how slippery the yarn is) and isn't noticeable

Here's one for two color join. She used a different ply, finer weight yarn for the second color just to show it could be done with different plies, but I wouldn't knit like that because a sudden change in weight could affect your gauge. http://www.youtube.com/#/watch?v=2-u...%3D2-u66X5RYjc

She says don't cut the ends till you're done and it's washed which I think is a good idea.

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Jan

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